Regression with more than one output, neural network
Welcome to AI-SE! Please use shorter description next time because it makes it hard to understand what you ask :)

I believe you want a neural network that can predict future values of multiple variables given multiple inputs. This belongs to the general time series forecasting problem.

One of the best neural network architectures that can handle this problem is the LSTM Recurrent Neural Network (LSTM-RNN). The reason I say "best" is because of their architecture that allows them to develop memory of what they have seen in the past and use it for future predictions. In other words they can cross-correlate in a linear/nonlinear fashion several past steps of multiple variables to future values of multiple other variables, like a black box.

No other neural network type does that. They are the only type of network that can learn the dynamics of a system.

An extremely useful tutorial for your purposes is this, please take a look.